In addition to Wictor's answer there are some rumors on the internet that you have to make sure you apply the "noindex" to nested DIV's as well. Just putting a "noindex" on the parent node isn't enough to make sure all child nodes are ignored as well. Each child node seems to be re-evaluated for the "noindex" class, according to various sources:
http://sharedknowledgepoint.com/2011/09/12/exclude-page-content-from-search-crawler/
http://blogs.msdn.com/b/markarend/archive/2010/06/07/control-search-indexing-crawling-within-a-page-with-noindex.aspx

I'm currently working on a FAST implementation (2010) and the above doesn't seem to apply there. I can put "noindex" on a top node and it will ignore everything below. Maybe it's a SharePoint/Search Server issue...